Constrained tracking of ground objects using regional measurements

ABSTRACT

A method for constrained tracking of objects using regional measurement. In one embodiment the system includes a plurality of sensors deployed in a region, wherein the sensors detect a mobile target. A first processing section receives target data from the sensors and processes target localization information. A second processing section linearly constrains the target localization information and generates a regional measurement which is filtered to generate an accurate target location.

RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.60/509,835 filed Oct. 8, 2003, and U.S. Provisional Application60/604,224 filed Aug. 24, 2004, both of these applications are hereinincorporated in their entirety by reference.

STATEMENT OF GOVERNMENT INTEREST

Portions of the present invention may have been made in conjunction withGovernment funding under contract number N66001-98-C8515 and there maybe certain rights to the Government.

FIELD OF THE INVENTION

The invention relates to tracking of objects, and more particularly, toa system of tracking targets using constrained tracking.

BACKGROUND OF THE INVENTION

There are numerous fields and applications related to tracking oftargets and the estimation of position/location of the targets at somefuture time based on mathematical equations. For example, Kalmanfiltering is an efficient computational (recursive) means to estimatethe state of a process, in a way that minimizes the mean of the squarederror and is very beneficial in that it supports estimations of past,present, and even future states, and it can do so even when the precisenature of the modeled system is unknown.

One of the applications is the detection of targets based on one or moresensors that attempts to locate an approximate position of a target atsome instant of time and track that target as it moves. Future positionestimates are calculated using certain a-priori information. There aremany variables that contribute to the overall calculations, and thestate of art is always attempting to refine the estimation process.

There are numerous types of sensors in the security, defense andmilitary implementations. Distributed unattended ground sensor (UGS)systems are used to meet a wide variety of program requirements relatedto the precision tracking of ground vehicles, persons/animals and otherobjects. The UGS sensors are inexpensive electronic devices that aredeployed in areas in which the detection of moving objects is desired.The sensor technology comes in many forms including acoustics,electrostatic, magnetic, optics, seismic, and imaging. There arenumerous detection modules that are known to those skilled in the artthat can be co-located with the UGS providing sensing and detectioncapability employing one or more detection types.

The UGS typically has a power source, one or more sensors, and acommunications section that are coupled together within an inexpensiveform factor. Some sensors even incorporate a processing section. Thesesmall units can be manually deployed or deployed by other means such asartillery and air deployment.

The UGS units typically are low power devices and therefore have alimited range for detection as well as transmission. A plurality ofUGS's can create a network of detection devices that can communicatewith each other and with a central location for processing data from allsuch sensors. Using an array of sensors can more accurately identify thelocation of a target and develop a grid for detection and tracking. Themicro-internetted unattended ground sensors (MIUGS) are examples ofnetworking within a community of deployed sensors.

A technique that is often used to assist in achieving high-precisiontracking of object such as ground vehicles is referred to as constrainedtracking. Constrained tracking is a procedure which utilizes a-prioriinformation based upon the likelihood that an object is traveling alonga given path. There are a number of methods for performing constrainedtracking of vehicles which are known to those skilled in the art, andrely on confining a tracking filter's state estimates based upon someusage of a-priori road information. If the likelihood of a vehicletraveling along a given path is high, then information related to theknown path can be used to assist in achieving improved trackingaccuracies.

Thus, typical methods for performing constrained tracking rely onconstraining the state estimate outputs of a tracking filter to a-prioriroad information. However, such methods often induce an adverse effectinto the closed-loop nature of the tracking filter's algorithm whichresults in degraded tracking performance when large spatial and/ordynamic constraints are required.

There have been numerous efforts in various fields that have madeprogress to suit the particulars of a specified application. Forexample, studies in automatic vehicle location (AVL) utilize processingtechniques that track vehicle, such as trucks. One implementation uses acommunications link from the vehicle to a central processing centerestablishes a perimeter about the truck in which the truck is supposedto travel. The concept of geo-fencing checks for anomalies that couldindicate truck problems or other unexpected difficulties if the truckposition breaches the established perimeter.

Unfortunately, the track constrained methods often induce an adverseeffect into the closed-loop nature of the tracking filter's algorithmwhich results in degraded tracking performance when large spatial and/ordynamic constraints are required. What is needed is a method forperforming constrained tracking which constrains the open-loopmeasurements supplied to the tracking filter. By constraining theopen-loop measurement data prior to being applied to the trackingfilter, the closed-loop algorithm structure of the tracking filterremains unaltered and the constrained tracking performance may be moreresponsive and robust.

BRIEF SUMMARY OF THE INVENTION

One embodiment of the present invention provides ameasurement-constrained approach to performing constrained tracking. Byconstraining the open-loop measurement data prior to being applied tothe estimator, the closed-loop nature of the estimator remains unalteredand the tracking performance is shown to be more responsive and robust.Thus, adverse closed-loop effects observed when constraining targettrack state estimate data to a-priori road information are eliminated.Such closed-loop effects are eliminated by constraining open-loopmeasurement information and applying constrained measurements to targettracking filter thus leaving closed-loop algorithm structure of trackingfilter unaltered.

One embodiment is a method for tracking mobile objects along a targetpath, comprising identifying a plurality of way-points along the targetpath and processing a position measurement of at least one object.Another step includes computing a distance parameter between theposition measurement and at least two of the way-points, and defining aroad segment between two of the way points that are closest to theposition measurement. Linearly constraining the measurement position tothe road segment and computing a regional measurement.

The method can further comprise determining a likelihood that theposition measurement is within a range of the target path, and computingthe position measurement without linearly constraining if the positionmeasurement is outside the range. The range can be fixed or astatistical distance such as a chi-square threshold.

The way-points are position coordinates and can be selected from atleast one of the group consisting of: pre-determined geographicalpositions and dynamically derived geographical positions.

The position measurement can be derived from triangulating a set ofbearing lines from at least two sensors. The position measurement canalso be transmitted from a repeater that relays the positionmeasurement.

There are typically a number of variables, and the computing can employat least one uncertainty variable, wherein the uncertainty variable isselected from at least one of the group consisting of a set of roadway-point uncertainties and a measurement covariance.

Other steps in the method may include applying the regional measurementto a tracking filter. Various filters can be used, and this includes thetracking filter being a constant gain and variable gain filter,including a Kalman filter.

A further embodiment includes an apparatus for tracking at least onemobile target, comprising a communications section, a memory device, anda microprocessor coupled to the communications section and the memorydevice. The microprocessor comprises a constrained measurement unit, andan estimator, wherein a target position measurement is linearlyconstrained by the constrained measurement unit prior to processing bythe estimator. The estimator can be any of the filter types known tothose skilled in the art, such as a Kalman filter. The microprocessorcan further comprise a fusion section that processes the target positionmeasurement from a set of sensor measurements received by thecommunications section. The system can also have a global positioningsystem (GPS) coupled to the microprocessor.

Another embodiment includes a system for tracking at least one mobiletarget in a region along a target path having way-points, comprising aplurality of sensors deployed in the region, wherein the sensors detectthe mobile target. A first processing section receives target data fromthe sensors and processes target localization information. A secondprocessing section is used, wherein the target localization informationis linearly constrained and generates a regional measurement. A thirdprocessing section filters the regional measurement and generates afiltered target position. The third processing section can include afilter such as a variable gain or constant gain filter. The filteredtarget position can be used to update a target track

The target data from the sensors can be at least two bearing lines andthe target localization information and is processed using triangulationfrom the bearing lines.

The target path can have threshold bounds and if the target localizationinformation is outside the threshold bounds, the target localizationinformation is not linearly constrained and the target localizationinformation establishes a non-constrained target position.

The first processing section can also receive target data from at leastone repeater unit that communicate with the sensors. The filtered targetposition may be communicated to a central processing center.

The features and advantages described herein are not all-inclusive and,in particular, many additional features and advantages will be apparentto one of ordinary skill in the art in view of the drawings,specification, and claims. Moreover, it should be noted that thelanguage used in the specification has been principally selected forreadability and instructional purposes, and not to limit the scope ofthe inventive subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic perspective showing a plurality of sensorsdeployed about a target traveling along a given path.

FIG. 2 is a flow chart diagram illustrating directional process noise(track-constrained approach).

FIG. 3 is a flow chart diagram illustrating pseudo-measurements(track-constrained approach).

FIG. 4 is a flow chart diagram illustrating one embodiment for regionalmeasurements (measurement-constrained approach).

FIG. 5 shows the target path and node configuration used forfield-tests.

FIG. 6 a illustrates test data for the spatial tracking performance forbaseline method of constrained tracking.

FIG. 6 b illustrates test data for the spatial tracking performance fordirectional process noise method of constrained tracking.

FIG. 6 c illustrates test data for the spatial tracking performance forpseudo-measurements of constrained tracking.

FIG. 6 d illustrates test data for the spatial tracking performance forregional measurement of constrained tracking.

FIG. 7 a illustrates the track error to truth for baseline method ofconstrained tracking.

FIG. 7 b illustrates the track error to truth for directional processnoise method of constrained tracking.

FIG. 7 c illustrates the track error to truth for pseudo-measurementmethod of constrained tracking.

FIG. 7 d illustrates the track error to truth for regional measurementmethod of constrained tracking.

FIG. 8 a graphically illustrates the directional process noise model.

FIG. 8 b graphically illustrates the pseudo-measurements model.

FIG. 8 c graphically illustrates the regional measurements model.

FIG. 9 is a block diagrammatic perspective of central command andcontrol.

FIG. 10 is a system flow chart for the regional constrained measurementsystem.

DETAILED DESCRIPTIONS OF THE INVENTION

Referring to FIG. 1, a plurality of sensors 15, 20, 25, 30 are deployedin a given region that indicates a road or expected track 5 as well asthe actual path or track 10 that is taken by a target 50. There are anumber of way-points W1, W2, W3, and W4 along the expected path 5 thatare pre-determined position points. Waypoints are geographicalcoordinates or locations used for positioning that can be previouslyrecorded and stored in the UGS or at the central command 70. They may becheck points on a route, significant ground features, data from otherUGS units, or a fully mapped region that allows for dynamic allocationof the waypoints. These way-points W1-W4 may be stored in memory withinthe central command 70 or the sensors 15, 20, 25, 30 and may also bedownloaded or updated to the units.

At any given time, one or more sensors 15, 20, 25, 30 may be able todetect the presence of the target vehicle 50 and provide some bearing orlocation data. The UGS units 15, 20, 25, 30 may have processingcapability to compute the constrained tracking computations or transmitdata to a central command and control processing center 70. In a typicalscenario, several sensors establish a bearing line 60 from the sensor tothe target. Each of the bearing lines 60 are communicated to the centralcommand or gateway 70 which uses the bearing lines to triangulate atarget position. A repeater (not shown) can relay the sensor data fromthe low-powered sensors to other sensors, gateways or central command toextend the geographic coverage.

There may be periods that the sensors 15, 20, 25, 30 may not detect thetarget 50 due to location of the target 50 or if the target otherwisebecome undetectable. The UGS units 15, 20, 25, 30 may also beintermittent in operation in relation to detection or transmission. Inany event, there may be periods where the target 50 location is unknownand estimates are required for present and future locations.

The present application describes three methods for performingconstrained tracking:

-   -   1. Directional Process Noise (track-constrained approach)    -   2. Pseudo-Measurements (track-constrained approach)    -   3. Regional Measurements (measurement-constrained approach)

Each of the three methods assume that some a-priori road information(way-points) have been collected prior to implementation. As describedherein, the simulation results illustrate that themeasurement-constrained approach is more responsive and robust then thetrack-constrained approaches.

Directional Process Noise

“Directional process noise” is a method of performing constrainedtracking which computes angular information between road way-points andadjusts the estimator's process noise to allow for more bandwidth alongthe expected direction of target motion and less bandwidth orthogonal tothe expected direction of target motion. A flow diagram for the“directional process noise” method is provided in FIG. 2.

The typical track-constrained approaches rely on constraining the stateestimate outputs of a tracking filter to a-priori road information.These methods tend to induce adverse effects into the closed-loop natureof the estimator resulting in degraded tracking performance when largespatial and/or dynamic constraints are required. Road way-points aretypically measured using some global position system (GPS) and stored inmemory locally or communicated as required.

The algorithm descriptions corresponding to each element in FIG. 2 areprovided herein. The first step 100 is the computing the statisticaldistance between road way-points and track estimates. Certaininformation is required for the processing, namely road-way points 102,road way-point uncertainties 104, track estimate 106 and track estimatecovariance. The road elements 102, road element uncertainties 104, trackestimate 106 and track estimate covariance 108 are processed in order tocompute the normalized distance parameters.

The processing commences as follows:Compute Statistical Distances Between Road Way-Points and Track Estimate100: $\begin{matrix}{D_{i} = {{v_{i}}^{\prime}S_{i}^{- 1}v_{i}}} \\{{{\text{for}\quad i} = 1},2,\ldots\quad,N} \\{{\underset{\_}{\text{where}} :: N} = \text{number~~of~~road~~way-points}} \\{v_{i} = \begin{bmatrix}{{rx}_{i} - \hat{x}} \\{{ry}_{i} - \hat{y}}\end{bmatrix}} \\{S_{i} = \left\lbrack {{HPH}^{\prime} + U_{i}} \right\rbrack} \\{H = {{observation}{\quad\quad}{matrix}}}\end{matrix}$

The track-to-road processing computes the normalized distance parametersbetween each road way-point and the desired track. Determine LikelihoodOf Track Estimate Being On-Road 110:D_(min) ₁ <χ₂ ²D_(min) ₂ <χ₂ ²

-   -   where:        -   D_(min) ₁ =first minimum statistical distance        -   D_(min) ₂ =second minimum statistical distance        -   χ₂ ²=chi-square threshold for two degrees of freedom

A road segment is defined based upon the two closest road way-points tothe desired track. The next step defines the road segment based uponminimum distance parameters. The processing commences as follows:

Locate Road-Segment Closest to Track Estimate 120:Rx₁=r_(xDmin) ₁Ry₁=r_(yDmin) ₁Rx₂=r_(xDmin) ₂Ry₂=r_(yDmin) ₂

-   -   where:        -   Rx₁, Ry₁=way-point corresponding to first minimum            statistical distance.        -   Rx₂, Ry₂=way-point corresponding to second minimum            statistical distance.

The next step computes the road segment orientation angle. Compute AngleOf Road-Segment With Respect to the estimator's reference frame 130:$\psi = {\tan^{- 1}\left( \frac{{Rx}_{1} - {Rx}_{2}}{{Ry}_{1} - {Ry}_{2}} \right)}$

It is then necessary to Rotate Road Segment Uncertainty Parameters IntoEstimator's Reference Frame 140 and compute the directional processnoise 150: $Q = {{\begin{bmatrix}{- {\cos(\psi)}} & {\sin(\psi)} \\{\sin(\psi)} & {\cos(\psi)}\end{bmatrix}\begin{bmatrix}\sigma_{o}^{2} & 0 \\0 & \sigma_{a}^{2}\end{bmatrix}}\begin{bmatrix}{- {\cos(\psi)}} & {\sin(\psi)} \\{\sin(\psi)} & {\cos(\psi)}\end{bmatrix}}$

-   -   where:        -   σ₀ ²=expected process noise variance orthogonal to            road-segment            -   σ_(a) ²=expected process noise variance along                road-segment

The Kalman filter process noise for the desired track is directionalizedalong the road segment. For example, the filter bandwidth along theassociated road segment is greater than the bandwidth orthogonal to theassociated road segment. The directionalized process noise constrainsthe track movement to be along the desired track segment.

Pseudo-Measurements

“Pseudo-measurements” is a method for performing constrained trackingwhich pre-defines a constraint zone and allows the estimator to freelyoperate within the boundaries of the constraint zone. Once theconstraint zone becomes violated, however, a pseudo-measurement isgenerated and applied to the estimator. The magnitude and uncertainty ofthe pseudo-measurement are selected such that the corrected stateestimate is placed on the constraint it violated, thus removing theinitial violation. The use of pseudo-measurements allows the constraintinformation to be introduced using the normal filtering action of anestimator, and, as a result, modifies both the conditional mean anderror covariance of the state estimate in a pseudo-consistent manner. Aflow diagram for the pseudo-measurements method is provided in FIG. 3.

The algorithm descriptions corresponding to each element in FIG. 3 areprovided below.Compute Statistical Distances Between Road Way-Points and Track Estimate200. $\begin{matrix}{D_{i} = {{v_{i}}^{\prime}S_{i}^{- 1}v_{i}}} \\{{{\text{for}\quad i} = 1},2,\ldots\quad,N} \\{{\underset{\_}{\text{where}} :: N} = \text{number~~of~~road~~way-points}} \\{v_{i} = \begin{bmatrix}{{rx}_{i} - \hat{x}} \\{{ry}_{i} - \hat{y}}\end{bmatrix}} \\{S_{i} = \left\lbrack {{HPH}^{\prime} + U_{i}} \right\rbrack} \\{H = {{observation}{\quad\quad}{matrix}}}\end{matrix}$

The track-to-road processing computes the normalized distance parametersbetween each road way-point and the desired track. Determine LikelihoodOf Track Estimate Being On-Road 210:D_(min) ₁ <χ₂ ²D_(min) ₂ <χ₂ ²

-   -   where:        -   D_(min) ₁ =first minimum statistical distance        -   D_(min) ₂ =second minimum statistical distance        -   χ₂ ²=chi-square threshold for two degrees of freedom

A road segment is defined based upon the two closest road way-points tothe desired track. The next step defines the road segment based uponminimum distance parameters. The processing commences as follows:

Locate Road-Segment Closest to Track Estimate 220:Rx₁=r_(x Dmin) ₁Ry₁=r_(yDmin) ₁Rx₂=r_(xDmin) ₂Ry₂=r_(yDmin) ₂

-   -   where:        -   Rx₁, Ry₁=way-point corresponding to first minimum            statistical distance.        -   Rx₂, Ry₂=way-point corresponding to second minimum            statistical distance.

The next step is to Compute Constraint Zone For Road-Segment 230:cz _(min) _(x) =min[Rx ₁ , Rx ₂]−σ_(cz)cz _(min) _(y) =min[Ry ₁ , Ry ₂]−σ_(cz)cz _(max) _(x) =max[Rx ₁ , Rx ₂]+σ_(cz)cz _(max) _(y) =max[Ry ₁ ,Ry ₂]+σ_(cz)

-   -   where:        -   cz_(min) _(x) =constraint zone x-axis minimum constraint        -   cz_(min) _(y) =constraint zone y-axis minimum constraint    -   cz_(max) _(x) =constraint zone x-axis maximum constraint    -   cz_(max) _(y) =constraint zone y-axis maximum constraint    -   σ_(cz)=constraint zone size parameter

Check For Constraint Violations and Generate Pseudo-Measurement(s) 240:$\begin{matrix}{z_{pm} = {cz}_{{nv}_{x,y}}} \\{R_{pm} = {C \cdot P_{v} \cdot C^{\prime} \cdot \left\lbrack \frac{{cz}_{{nv}_{x,y}} - {C \cdot {\underset{\_}{\hat{x}}}_{v}}}{{cz}_{v_{x,y}} - {C \cdot {\underset{\_}{\hat{x}}}_{v}}} \right\rbrack}}\end{matrix}$

-   -   where:        -   z_(pm)=pseudo-measurement (set to non-violated constraint)        -   R_(pm)=pseudo-measurement covariance        -   C=pseudo-measurement observation matrix        -   {circumflex over (x)} _(v)=state estimate violating            constraint        -   P_(v)=state estimate covariance violating constraint        -   cz_(v) _(x,y) =violated constraint        -   cz_(nv) _(x,y) =non-violated constraint

Update State Estimate and Covariance with Pseudo-Measurement(s) 250 andGenerate the Constrained State Estimate 260:{circumflex over (x)} _(c) ={circumflex over (x)} _(v) +[P·C′·(C·P·C′+R_(pm))⁻¹ ]·[z _(pm) −C·{circumflex over (x)} _(v)]P _(c) =P _(v) −[P·C′·(C·P·C′+R _(pm))⁻¹ ]·C·P _(v)Regional Measurements

“Regional measurements” is a method of performing constrained trackingwhich linearly constrains the open-loop measurement data prior to beingapplied to the estimator. This method of performing constrained trackingallows the closed-loop nature of the estimator to remain unaltered whiledriving the performance and robustness of the estimator solely basedupon the accuracy of the measurement and measurement covarianceinformation. A flow diagram for the “regional-measurements” method isprovided in FIG. 4.

The depicted embodiment of the present invention in FIG. 4 describes ameasurement-constrained approach to achieving high-precision tracking asopposed to the typical track-constrained approaches. The typicalconstrained tracking approaches, such as directional process noise andpseudo-measurements use a-priori road information that is collected andused to constrain the state estimates of a tracking filter when there isa ‘high’ likelihood that a given vehicle is traveling along some knownpath. The typical track-constrained approach has difficulty inaccurately updating the estimator's covariance to reflect the level ofconstraint applied to the state estimates. When the state estimate of atracking filter is constrained to a-priori road information, thecovariance describing the improved uncertainty is not consistent withthe level of constraint applied to the state estimate data. As a result,adverse effects may be induced into the closed-loop nature of theestimator resulting in degraded tracking performance when large spatialand/or dynamic constraints are required.

Thus, a better methodology of performing constrained tracking is toconstrain the open-loop measurements supplied to the estimator. Byconstraining the open-loop measurement data prior to being applied tothe estimator, the closed-loop nature of the estimator remains unalteredand the performance and robustness of the estimator is solely drivenbased upon the accuracy of the measurement and measurement covarianceinformation.

The algorithm descriptions corresponding to each element in FIG. 4 areprovided herein. Certain information is used for the processing, namelyroad-way points 402 which as already explained are predeterminedposition points that can be static or dynamic. The road way-pointuncertainties 404 relates to the level of accuracy associated with theroad way point position point. The Measurement 406 refers to theposition estimate. And, track measurement covariance 408 relates to theamount of uncertainty for the measurement such as the triangulationuncertainty using bearing lines from the sensors.

The Processing Commences with Computing Statistical Distances BetweenRoad Way-Points and Measurement 400: $\begin{matrix}{D_{i} = {v_{i}^{\prime}S_{i}^{- 1}v_{i}}} \\{{{{for}{\quad\quad}i} = 1},{2\ldots}\quad,N}\end{matrix}$ $\begin{matrix}{{{where} :: \quad N} = \text{number~~of~~road~~way-points}} \\{v_{i} = \begin{bmatrix}{{rx}_{i} - z_{x}} \\{{ry}_{i} - z_{y}}\end{bmatrix}} \\{S_{i} = \left\lbrack {R + U_{i}} \right\rbrack}\end{matrix}$

The measurement processing computes the normalized distance parametersbetween the road way-point and the desired measurement. DetermineLikelihood Of Track Estimate Being On-Road 410:D_(min) ₁ <χ₂ ²D_(min) ₂ <χ₂ ²

-   -   where:        -   D_(min) ₁ =first minimum statistical distance        -   D_(min) ₂ =second minimum statistical distance    -   χ₂ ²=chi-square threshold for two degrees of freedom

A road segment is defined based upon the two closest road way-points tothe desired measurement. The next step defines the road segment basedupon minimum distance parameters. The processing commences as follows:

Locate Road-Segment Closest to Measurement 420:Rx₁=r_(xDmin) ₁Ry₁=r_(yDmin) ₁Rx₂=r_(xDmin) ₂Ry₂=t_(yDmin) ₂

-   -   where:        -   Rx₁, Ry₁=way-point corresponding to first minimum            statistical distance.        -   Rx₂, Ry₂=way-point corresponding to second minimum            statistical distance.            Compute Linear Constraint Coefficients 430:            α₁=1.0−α₂            α₂=0.5·(D _(min) ₁ /D _(min) ₂ )            Linearly Constrain Measurement Data to Road-Segment 440 and            Compute the Regional Measurement 450:            z _(rm) _(z) =α₁ ·RX ₁+α₂ ·RX ₂            z _(rm) _(y) =α₁ ·RY ₁+α₂ ·RY ₂            R _(rm) =R·(D _(min) ₁ /D _(min) ₂ )            Simulation Results

All performance results provided in this work are based upon actualfield-test data. For the simulation data set evaluated in this work, allmethods for constrained tracking produced identical track initiation andtrack duration results. Consequently, the primary metric of interestconsidered for this work was track accuracy.

The target path and node configuration used for the field test areillustrated in FIG. 5. The true target starts at “12:00” and traversescounter-clockwise one complete revolution. The nodes 500 represent thearray of deployed sensors. The way-points 510 are along the target pathand depict pre-determined measurement points. The way-points can bestatic or dynamically allocated if the region has been mapped. Thetarget path is generally processed having a bandwidth or range that canbe dynamically calculated based on certain parameters such as noise orset to a fixed value. The axes of the graph represent Northing andEasting in meters for two-dimensional tracking.

The parameters utilized for each method of constrained tracking areprovided herein, namely:

Directional Process Noise:

-   -   χ₂ ²=3.0    -   σ_(o)=0.0 meters    -   σ_(a)=100.0 meters        Pseudo-Measurements:    -   χ₂ ²=3.0    -   σ_(cz)=1.0 meter        Regional Measurements:    -   χ₂ ²=3.0

FIGS. 6 a-6 d illustrates the spatial tracking performance for eachmethod of constrained tracking. FIG. 6 a is the baseline for the spatialtracking performance and as noted, the baseline track 600 travels aboutthe target path of way-points 510 and deviating at certain points duringthe counter-clockwise path. This baseline track 600 represents thetracking performance without any form of constrained tracking appliedand is presented for comparison purposes.

FIG. 6 b represents the test data for the directional process noisemethod. The track 610 for the directional process noise processinggenerally follows the way-points 510 however it deviates from the targetpath on several instances. As noted, there is considerable ‘noise’ orjitter on the estimates and the track 610 barely makes the turn at thetop right.

FIG. 6 c represents the test data for the pseudo measurements scheme.The track 650 for the pseudo measurement processing generally followsthe path outlined by the way-points 510 deviating as indicated. Whilethe pseudo measurement track 650 has less jitter, it is unable to makethe turn at the top right.

FIG. 6 d shows the test data for the regional measurements according toone embodiment of the present invention. The track 660 for the regionalmeasurement processing closely follows the way-point path and thewaypoints 510 are essentially covered throughout the path. This visuallydemonstrates that the regional measurements methodology provides theclosest tracking as there is no jitter and it does make the turn at thetop right.

FIGS. 7 a-7 d illustrates the track error with respect to truth for eachmethod of constrained tracking.

FIG. 7 a shows the track error for the baseline testing. The CircularError Probability (CEP) for the baseline test is 22.68 meters. TheEasting error 700 and Northing error 710 depict the tracking error asmeasured in meters over the time interval (seconds) for thecounter-clockwise travel of the target along the path. The baselinetrack shows a larger error especially at the turn at approximately180-200 seconds.

FIG. 7 b shows the track error for the directional process noisetesting. The Circular Error Probability for directional process noisetest is 13.89 meters. The Easting error 720 and Northing error 730depict the tracking error as measured in meters over the time interval(seconds) for the counter-clockwise travel of the target along the path.As shown, there is considerable noise and a large error especially atthe turn.

FIG. 7 c shows the track error for the pseudo measurements testing. TheCircular Error Probability for the pseudo measurements test is 13.38meters. The Easting error 740 and Northing error 750 depict the trackingerror as measured in meters over the time interval (seconds) for thecounter-clockwise travel of the target along the path. While the pseudomeasurement track has less noise, it does possess significant error atthe turn.

FIG. 7 d shows the track error for the regional measurements testing.The Circular Error Probability for the regional measurements test is9.30 meters. The Easting error 760 and Northing error 770 depict thetracking error as measured in meters over the time interval (seconds)for the counter-clockwise travel of the target along the path. As shown,the regional measurement scheme has less noise and minimal error at theturn.

Thus, FIGS. 6 a-d and 7 a-d graphically depict that the regionalmeasurements method of constrained tracking provides the best trackingaccuracy along with the most amount of responsiveness and robustness.

Referring to FIG. 8 a, the processing according to directional processnoise is graphically illustrated. As described herein, the directionalprocess noise allows target motion along the selected road segment andrestricts target motion orthogonal to the selected road segment bycontrolling the estimator's process noise model. The estimator's processnoise is modified by computing the angle of the selected road segment,ψ, with respect to the reference frame and rotating the road segmentuncertainty parameters, σ_(a) ² and σ_(o) ², into the estimators processmodel, σ_(x) ² and σ_(y) ². By selecting σ_(a) ²>>σ_(o) ², thedirectional process noise technique provides more uncertainty(bandwidth) along the road segment and less uncertainty (bandwidth)orthogonal to the road segment resulting in constrained target motionrelative to the selected road segment.

The reference frame 800 establishes the X/Y coordinate system forprocessing and can be absolute or relative. The way-points 805 are shownalong the target path 810. The selected road segment 815 represents thesection between two waypoints 800 for processing the target estimate820.

FIG. 8 b shows the processing according to pseudo-measurements scheme.As described herein, the pseudo-measurements allow the estimator tofreely operate within boundaries of a predefined constraint zone. Oncethe constraint zone is violated or breached, a pseudo-measurement isgenerated and applied to the estimator. The magnitude and uncertainty ofthe pseudo-measurement is selected such that the constrained stateestimate is placed on a violated constraint thereby removing the initialviolation. The pseudo-measurement is applied using normal filteringaction of the estimator and modifies both conditional mean andcovariance in a pseudo-consistent manner.

The reference frame 800 establishes the X/Y coordinate system forprocessing and can be absolute or relative. The way-points 805 are shownalong the target path 810. The selected road segment 815 represents thesection between two waypoints 800. The constraint zone 850 representsthe bounded-region wherein the estimator operates without anyconstraints. When there is a track estimate violation 835 that isoutside of the constraint zone 850, the pseudo-measurement processing isperformed and applied to the estimator thereby generating a constrainedtrack estimate 830.

Referring to FIG. 8 c, the regional measurement system is graphicallydepicted. The regional measurements linearly projects open-loopmeasurement data onto the selected road segment prior to being appliedto the estimator. The closed-loop nature of the estimator remainsunchanged and the performance and robust nature of the estimator isdriven by the accuracy of measurement and measurement covarianceinformation.

The reference frame 800 establishes the X/Y coordinate system forprocessing and can be absolute or relative. The way-points 805 are shownalong the target path 810. The selected road segment 815 represents thesection between two waypoints 805 as detailed herein.

As described here, the sensor data is used to derive the Measurement850. The Statistical Distances Between Road Way-Points And, Measurement850 is computed for the two closest way-points 805 according to theformula below, and the resultant statistical distance is shown as D₁ andD₂: $\begin{matrix}{D_{i} = {v_{i}^{\prime}S_{i}^{- 1}v_{i}}} \\{{{{for}\quad i} = 1},{2\ldots}\quad,N} \\{{{where}:\quad N} = \text{number~~of~~road~~way-points}} \\{v_{i} = \begin{bmatrix}{{rx}_{i} - z_{x}} \\{{ry}_{i} - z_{y}}\end{bmatrix}} \\{S_{i} = \left\lbrack {R + U_{i}} \right\rbrack}\end{matrix}$

The measurement processing then determines the likelihood that theMeasurement 850 is on-road or off-road by applying a chi-squarethreshold to D1 and D2.D_(min) ₁ <χ₂ ²D_(min) ₂ <χ₂ ²

-   -   where:        -   D_(min) ₁ =first minimum statistical distance        -   D_(min) ₂ =second minimum statistical distance    -   χ₂ ²=chi-square threshold for two degrees of freedom

The constrained tracking is only pursued if D1 and D2 are within thechi-square threshold bounds, otherwise the measurement data is processedwithout constraints.

A road segment 815 is then defined based upon the two closest roadway-points 805 to the measurement 850. The road segment 815 is basedupon minimum distance parameters, and the processing commences asfollows:

Locate Road-Segment Closest to Measurement:Rx₁=r_(xDmin) ₁Rx₂=r_(xDmin) ₁Ry₂=r_(yDmin) ₂Ry₂=r_(yDmin) ₂

-   -   where:        -   Rx₁, Ry₁=way-point corresponding to first minimum            statistical distance.        -   Rx₂, Ry₂=way-point corresponding to second minimum            statistical distance.

The processing continues with computing the linear constraintcoefficients to be used for the constrained measurement. Thecoefficients are derived as follows:α₂=0.5·(D _(min) ₁ /D _(min) ₂ )α₁=1.0−α₂

Once the linear coefficients have been processed, the next step is tolinearly constrain the Measurement 850 To Road-Segment 815 and computethe regional constrained measurement 855:z _(rm) _(x) =α₁ ·RX ₁+·α₂ ·RX ₂z _(rm) _(y) =α₁ ·RY ₁+α₂ ·RY ₂R _(rm) ^(=R)·(D _(min) ₁ /D _(min) ₂ )

FIG. 9 illustrates a simplified embodiment of central command andcontrol 900. There is an antenna 905 and communications section 910 thatis responsible for receiving and transmitting data and instructions toand from at least one sensor (not shown). The data may also betransmitted to other control centers in processed form or as raw data.

The data from the one or more sensors (not shown) is received by theantenna 905 and processed by the communications section 910 to providethe digital data to the processing section 915. It is common for thedata to be amplified and filtered prior to processing by themicrocomputer 915. The processing within the microprocessor 915commences as described herein and reads/stores data to the memorysection 910 as needed.

The processing section 915 includes a fusing section 917, constrainedmeasurement processing section 918 and the estimator 919. The regionalmeasurements processing accepts target localization (position)information. If target localization information is not directlyavailable, as in a bearing-only system, then some form of data fusion917 is required to transform the available information into targetlocalization (position) information. The regional measurement processingconstrains the provided target localization information 918 and sendsthe constrained result to an optimal tracking filter or estimator 919,for additional filtering and reduction in target location uncertainty.The filter types include any of the constant gain or variable gainfilter including Kalman filters.

According to one embodiment of the present invention, the constrainedopen-loop measurement data from the fusing section 917 is applied by theconstrained measurement section 918 before the data is processed by thetracking filter or estimator 919. The tracking filter or estimator 919accepts constrained position and uncertainty data provided by theregional measurement processing which is used to compute a weightingfactor depending upon the uncertainty level of the constrained regionalmeasurement. For example, a noisy or higher degree of uncertainty for agiven linearly constrained position will lower the weighting factorutilized by the filter. The improved position data from the estimator919 is used for estimating future positions in order to provide anupdated position measurement.

The system 900 can employ a GPS unit 925 which not only provides thegeographic location data but also a precision clock.

Power unit 940 provides the necessary power to the components of thecontrol unit 900. The power can be external AC source from a power lineor generator or from various other power sources known to those skilledin the art such as batteries and solar energy.

The system gateway processing in one embodiment can be expressed asillustrated in FIG. 10, wherein the gateway or central processing unitreceives sensor measurement data 950 from the various sensors and/orsub-system gateways. As described herein, the sensor data can be bearinglines from at least one sensor that is transmitted directly to thecentral processing unit or to retransmitted from another gateway device.The collected measurements are processed to locate one or more targetposition using techniques such as triangulation schemes. The targetmeasurements are then processed as described herein to associate thetarget location measurements to the tracks 955. If the targetmeasurements associate with one or more tracks 960, then regionalmeasurement processing is applied 975 as further detailed in theaccompanying description of FIG. 4 and the constrained measurementresult is sent to the tracking filter or estimator for additionalfiltering and reduced uncertainty in target location 980.

If the target measurements do not associate with one or more tracks 960,then the non-associated measurement data is used to initiate new targettracks 965. Once all measurements have been used to update existingtracks 980 or initiate new tracks 965, then standard track maintenanceroutines 970 such as track combination, track termination and trackpropagation are performed for future processing. Track terminationrefers to the processes associated with the merger or cancellation ofcertain tracks. The track propagation refers to a number of processesand includes forwarding the optimized position measurements to predictthe next expected positions. It should be readily apparent that havingknowledge of positions and time can be used to process velocity (changein distance divided by change in time) and even acceleration (change invelocity divided by change in time).

For comparison purposes, the constrained processing under thedirectional process noise is generally performed when performing trackmaintenance. Likewise, the pseudo-measurement technique is typicallyincorporated into the system when updating the track with measurementdata.

In one working embodiment, the present invention is implemented with agateway that communicates with a plurality of UGS devices. Thetechnology and variations of UGS are well known to those in the art andmay have are one or more sensing units coupled to a UGS microprocessor,a memory section, a GPS unit, and a communications section. A powersupply such as a battery, solar or other power source provide thenecessary power for the UGS. The UGS sensing units can be any of thesensor types known in the art such as optical, magnetic, seismic, andacoustic as well as any combination thereof. There may be analog-digitalprocessing for analog sensors in order to place the data in a formatusable by the rest of the system. The UGS microprocessor can control thefunctionality of the unit and transmit data via the communicationssection to the gateway. There may be a number of gateway units deployedin the region that gathers data from a number of UGS units andre-transmits the data to a central gateway or controlling center. Inthis fashion the gateways act as repeaters that relay sensor data as thesensors generally have low power capabilities.

The processing section that processes data from the UGS sensors, such asbearing lines, calculates or triangulates the target position. Theposition measurement is analyzed to determine if it is a reasonabletarget location in order to assess whether to constrain tracking orallow for non-constrained measurements. The bounds of the target pathare generally normalized statistical measurements although various roadbounds can be used, wherein the system assesses whether the processedposition is close enough to the road to be constrained. If theconstrained tracking is employed, the regional measurement linearlyprojects open-loop measurement data onto selected road segments prior tobeing applied to the estimator. The closed loop nature of the estimatorremains unchanged. If the tracking measurement is ‘off-road’, theprocessing is unconstrained and processed without the constraints.

As is known to those skilled in the art, Kalman filtering is basicallydescribed as X_(k+1)=X_(k)+G(X_(k)−m). It is generally understood thatdirectional process noise techniques substantially rely on the Kalmanfilter. Likewise, pseudo-measurements also tend to be heavily dependenton Kalman filtering. However, the regional measurement system of thepresent invention is not bound to Kalman filtering and other filteringtypes are within the scope of the invention. Any of the variable gain orconstant gain filters may be employed with the present invention.

The foregoing description of the embodiments of the invention has beenpresented for the purposes of illustration and description. It is notintended to be exhaustive or to limit the invention to the precise formdisclosed. Many modifications and variations are possible in light ofthis disclosure. It is intended that the scope of the invention belimited not by this detailed description, but rather by the claimsappended hereto.

1. A method for tracking mobile objects along a target path, comprising:identifying a plurality of way-points along the target path; processinga position measurement of at least one object; computing a distanceparameter between said position measurement and at least two of saidway-points; defining a road segment between two of said way pointsclosest to said position measurement; and linearly constraining saidmeasurement position to said road segment and computing a regionalmeasurement.
 2. The method according to claim 1, further comprisingdetermining a likelihood that said position measurement is within arange of said target path, and computing said position measurementwithout said linearly constraining if said position measurement isoutside said range.
 3. The method according to claim 2, wherein saidrange is a chi-square threshold.
 4. The method according to claim 1,wherein said way-points are position coordinates are selected from atleast one of the group consisting of: pre-determined geographicalpositions and dynamically derived geographical positions.
 5. The methodaccording to claim 1, wherein said position measurement is derived fromtriangulating a set of bearing lines from at least two sensors thatdetects said object.
 6. The method according to claim 1, wherein saidcomputing employs at least one uncertainty variable, said uncertaintyvariable selected from at least one of the group consisting of: a set ofroad way-point uncertainties and a measurement covariance.
 7. The methodaccording to claim 1, further comprising applying said regionalmeasurement to a tracking filter.
 8. The method according to claim 7,wherein said tracking filter is selected from at least one of the groupconsisting of: a variable gain filter and a constant gain filter.
 9. Themethod according to claim 1, wherein said processing said positionmeasurement is transmitted from a repeater.
 10. An apparatus fortracking at least one mobile target, comprising: a communicationssection; a memory device; and a microprocessor coupled to saidcommunications section and said memory device, wherein saidmicroprocessor comprises a constrained measurement unit, and anestimator, wherein a target position measurement is linearly constrainedby said constrained measurement unit prior to processing by saidestimator.
 11. The apparatus according to claim 10, wherein saidmicroprocessor further comprises a fusion section that processes saidtarget position measurement from a set of sensor measurements receivedby said communications section.
 12. The apparatus according to claim 10,further comprising a global positioning system coupled to saidmicroprocessor.
 13. The apparatus according to claim 10, wherein saidestimator employs a filter selected from at least one of the groupconsisting of: a variable gain filter and a constant gain filter.
 14. Asystem for tracking at least one mobile target in a region along atarget path having way-points, comprising: a plurality of sensorsdeployed in the region, wherein said sensors detect said mobile target;a first processing section that receives target data from said sensorsand processes target localization information; a second processingsection wherein said target localization information is linearlyconstrained and generates a regional measurement; and a third processingsection that filters said regional measurement and generates a filteredtarget position.
 15. The system according to claim 14, wherein saidtarget data from said sensors is at least two bearing lines and saidtarget localization information is processed using triangulation fromsaid bearing lines.
 16. The system according to claim 14, wherein saidfiltered target position updates a target track.
 17. The systemaccording to claim 14, wherein said third processing section employs atracking filter selected from at least one of the group consisting of: avariable gain filter and a constant gain filter.
 18. The systemaccording to claim 14, wherein said filtered target position iscommunicated to a central processing center.
 19. The system according toclaim 14, wherein said target path has a threshold bounds and if saidtarget localization information is outside said threshold bounds, saidtarget localization information is not linearly constrained and saidtarget localization information establishes a non-constrained targetposition.
 20. The system according to claim 14, wherein said firstprocessing section receives target data from at least one repeater unitthat communicates with said sensors.